Physiological signals often appear as a sum of complicated processes of various affecting variables. A physiological signal may also be cyclical, i.e. repeating itself with respect to some of the variables. As a result of the foregoing, each single cycle of the signal carries information of a physiological phenomenon, but the physiological signal will differ from cycle-to-cycle due to variations in other affecting variables. A problem with such signals is that single cycle information may be noisy or may reflect only a short temporary state, whereas the extraction of useful clinical information may require signal averaging over a longer period of time and over multiple cycles.
Breathing is an example of such a cyclic process. Breathing comprises the inspiration and expiration phases of a respiratory cycle. Every breath can be characterized with different variables such as breath volume or duration and time division ratio between inspiration and expiration. A given breath may also affect subsequent breaths. In spontaneous breathing these variables may distribute to a broad range of values and successive breaths may be very different from each other.
Breathing gas composition is also characterized with different variables. Inspired breathing gases are typically a mixture of oxygen and nitrogen, i.e. air. In the lungs, oxygen is taken up into circulating blood and carbon dioxide (CO2) is released from the blood to the breathing gases in the lungs. Thus, the expired breathing gases also include CO2. Expiration gas composition varies in the course of expiration. At the beginning of expiration, the expired gases comprise mainly the inspiration breathing gases remaining in the airways at the end of the previous inspiration. Subsequently expired breathing gases comprise gases from the alveolar portions of the lungs. The alveolar gas CO2 concentration is a flow-weighted average of the gas concentrations from different lung regions. Flow rates from the lung regions vary according to variations in local pressure, compliance, and flow resistance. These determine the ventilation of a region of the lungs. Regional gas composition depends on the ratio of ventilation and blood perfusion of the region. The higher the rate of change of the gases in the gas space of a region (ventilation) and the lower the blood perfusion passing through the region, the lower the CO2 concentration and the higher the oxygen concentration in the gases will be. The regional expiration flow rate, as well as the ventilation/perfusion ratio, varies in different lung-related sicknesses. The resulting expiration gas composition profile over the course of expiration is thus characteristic for these sicknesses, and this profile can be used for diagnostic purposes.
Capnography measures breathing gas CO2 concentrations. In routine bedside use, the concentration is measured over time showing a pattern of breathing respiratory cycles divided into inspiration and expiration phases. By combining capnographic measurement during expiration with a spirometric measurement of breath volume, a volumetric capnograph (VCap) may be generated. Such a capnograph is a signal profile relating CO2 concentrations to expired breathing gas volume.
VCap has been combined with a measurement of arterial blood CO2 partial pressure (PaCO2) obtained from a blood sample using a blood gas analyzer. In an ideal lung without shunt and alveolar dead-space, a CO2 measurement at the end of expiration, i.e. an end tidal CO2 measurement (EtCO2), is very close to PaCO2. However, in various sicknesses the PaCO2-EtCO2 difference increases. The slope of the VCap alveolar expiration curve may also increase. For comparison, arterial sampling and the expiration breathing pattern have to be coincidental. Blood transit time from the lungs to arteries reachable for sampling is about 10-20 seconds. During this period, a couple of breaths variable in volume and duration may occur. This results in variations in dissolved gas concentrations in the blood. There may also be significant gas composition variations between successive breaths. To be able to compare the arterial dissolved gas concentrations with those of the breathing gases, the signals corresponding to the measured quantities have to be averaged over a period of time sufficient to even out the cyclical signal variations.
A problem in extracting a characteristic gas concentration profile from cyclically variable signals obtained during expiration is presented in FIG. 1 showing a simplified example of signals from two expirations in solid black lines. The two expirations vary in volume. A first of the breaths marked with (x) and reference number 10 is about 430 mL in volume and the second marked with (o) and reference numeral 12 is about 600 mL. Such variation is commonly found in spontaneous breathing. A characteristic for the smaller volume breath 10 is a higher expiration CO2 concentration profile compared to that of the larger volume breath 12. CO2 concentration is shown on the abscissa, scaled in CO2 partial pressure (PCO2) in millimeters of mercury (mmHg). A large expiration is typically preceded by a large inspiration that dilutes the alveolar gas concentration more effectively, resulting in a lower CO2 concentration profile for expiration 12. Assuming the arterial blood is sampled during these two breaths, an average CO2 reading of the breaths from which the cyclic variation shown in FIG. 1 has been eliminated is needed for comparing the blood and breathing gas CO2 concentrations for diagnostic purposes.
In FIG. 1, the solid line 14 represents the average calculated for expirations 10 and 12 for each increment of volume extending along the abscissa. At 430 ml the small volume breath 10 ends and the rest of the average curve up to the volume of the larger breath 12 follows the larger breath. At the end of smaller breath a distortion occurs in the average curve 14. This distortion reflects the difference in expired breathing gases volumes rather than the CO2 concentration properties of the expiration. Thus the slope calculated for the VCap alveolar expiration curve does not reflect the true lung expiration profile. Also the tidal volume (VT) and breath end-tidal CO2 (EtCO2) concentration will be misleading for comparison to the arterial CO2 (PaCO2).